6:39 One of my professors would use: W.W.T.S., 'for we want to show'. The initials you use have another meaning you don't want to imply. You are such a pleasure to watch. Keep doing the great work you are already doing.
This is basically a shorter version of the solution, that I posted under the original video. 👍 I converted the original equation to ⌈x² - x⌉ + 1 = x² + x + 1 and subtracted 1 on both sides to get ⌈x² - x⌉ = x² + x. Then I took the extra step of analyzing the functions beforehand and ruled out x < 0 that way. So I only checked for x² + x < x² - x + 1, which resolves into x < 1/2. My proof, that 0 < x < 1/2 leads to no solutions was a little different: Since x² ≤ x for 0 ≤ x < 1, the left hand side ⌈x² - x⌉ becomes ⌈-1 < x² - x ≤ 0⌉ = 0, making x = 0 the only solution.
I always enjoy your videos. You do a great job explaining everything. I think a more interesting equation is ceil(x^2-x+1) = x^2+x-1. It actually has two solutions.
Very cool, you can solve more difficult and interesting equations using a similar trick. For example, you might find that the equation below has three different real roots. floor(x^2 - x + 3) = x^2 + x - 1
Huh... I wondered about this and assumed it'd just be the floor/ceiling of both real and imag parts. I could see it being something different but am surprised it's simply "undefined".
Unfortunately for you, you cannot choose what I say for me. I think you'd be happy if you restrict your desires to where you have control. And please, don't make comments like this anywhere you don't have to be.
I am impressed by your honesty.
Ceil(x) = x+a [0
6:39 One of my professors would use: W.W.T.S., 'for we want to show'. The initials you use have another meaning you don't want to imply. You are such a pleasure to watch. Keep doing the great work you are already doing.
Yoh, I was total confused about the previous one . Thanks once again Mr Prime Newton.
Excellent !
Your explanation was easy to understand. 🇯🇵🇯🇵
This is basically a shorter version of the solution, that I posted under the original video. 👍
I converted the original equation to ⌈x² - x⌉ + 1 = x² + x + 1 and subtracted 1 on both sides to get ⌈x² - x⌉ = x² + x.
Then I took the extra step of analyzing the functions beforehand and ruled out x < 0 that way.
So I only checked for x² + x < x² - x + 1, which resolves into x < 1/2.
My proof, that 0 < x < 1/2 leads to no solutions was a little different:
Since x² ≤ x for 0 ≤ x < 1, the left hand side ⌈x² - x⌉ becomes ⌈-1 < x² - x ≤ 0⌉ = 0, making x = 0 the only solution.
U are a good guy and a Very different Máster.... Congratulations!
You're the best for this! Takes a lot to admit a mistake, let alone publicly.
I always enjoy your videos. You do a great job explaining everything. I think a more interesting equation is ceil(x^2-x+1) = x^2+x-1. It actually has two solutions.
Lovely 😍
Very cool, you can solve more difficult and interesting equations using a similar trick. For example, you might find that the equation below has three different real roots.
floor(x^2 - x + 3) = x^2 + x - 1
Best math youtuber on youtube imo.
Perfect🎉
Now its ok. Congratulations
Same question I wrote last year in my calculus 1 test.
Are floor and ceiling defined for complex numbers?
No it isn't defined for Complexes. These functions are real function so not valid for complex numbers.
Huh... I wondered about this and assumed it'd just be the floor/ceiling of both real and imag parts. I could see it being something different but am surprised it's simply "undefined".
Excelente 👍
It is a much better version thanks :)
Interesting, but is there any application?
Fun
niceeeee hahahaaaa
I just found a new meaning for WTF 😂😂
WTF means Welcome To Finland, because Finland offers so many WTF moments for foreigners.
Maybe just know
Ciel(f(x) + k) = Ciel(f(x)) + k
Therefore
Ciel(x² - x + 1) = x² + x + 1
Ciel(x² - x) + 1 = x² + x + 1
Ciel(x² - x) = x² + x
Ciel(x(x - 1)) = x(x + 1)
And now it is clear.
Hello. I still don't understand why we added ½. I'm sorry 😢.
I loved the video an explanation, I'm just disappointed about the triviality of the solution
Nice I solved correctly
The only REAL solution? How would you even define the ceiling for a non-real complex number?
Only solution.
Description says floor instead of ceiling
title has -1,
I enjoy hearing you talk about mathematics, but whether you just came home is your life, not mathematics. I don't want to hear about that.
Unfortunately for you, you cannot choose what I say for me. I think you'd be happy if you restrict your desires to where you have control. And please, don't make comments like this anywhere you don't have to be.